"Can I get your attention in that Trumbo deal for Skaggs and Eaton?" he remembered writing.
"Sure, why don't you come down and talk?" Dipoto quickly replied, according to Towers.
Two days later, a three-team trade fell into place.
Chicago acquired outfielder Adam Eaton from Arizona for left-hander Hector Santiago, and the Diamondbacks then sent Santiago and left-hander Tyler Skaggs to the Angels for slugger Mark Trumbo. Arizona also will receive a player to be named or cash from each of the other clubs.
"It's nice when you're able to have three clubs up here all feeling good about things," Hahn said Tuesday during a news conference. "Obviously, as Jerry pointed out, it does hurt a little bit, but it costs something to get something."
Trumbo, 27, hit .234 with 34 home runs and 100 RBIs this year, playing first base in 123 games because Albert Pujols was hurt. Despite hitting 95 homers during the last three seasons, the sometimes outfielder was deemed superfluous by Los Angeles, which craved starting pitching behind Jered Weaver, C.J. Wilson and Garrett Richards.
"Right now we'd line up with both guys as starters," Dipoto said.
Trumbo was used to hearing his name in trade talk.
"I think it's been rumored for years now," he said.
He'll join a batting order that includes Paul Goldschmidt, who led the NL with 125 RBIs and tied for the league lead in home runs with 36.
"We all addressed some of our biggest needs," Towers said. "We'll give him some protection."
After finishing last in the AL Central with their worst record since 1970 at 63-99, the White Sox were looking to make changes, and Hahn is counting on Eaton to provide a spark.
"We lacked a little bit of energy and a little edge," Hahn said. "This is a dirt-bag baseball player. This is a guy who has been described to me by someone at this table with words I can't use."
Santiago, 25, was 4-9 with a 3.56 ERA in 23 starts and 11 relief appearances. His fastball velocity has dipped from 93.8 mph in 2011 to 92.8 in 2012 to 91.8 last season, according to fangraphs.com.
Eaton, a 25-year-old speedy leadoff hitter, was sidelined from spring training until July 9 by a sprained left elbow. He hit .252 with three homers, 22 RBIs and 44 strikeouts in 250 at-bats for the Diamondbacks this year.
Skaggs, 22, went to Santa Monica High School, was taken by the Angels with the 40th overall selection of the 2009 amateur draft and was dealt to the Diamondbacks in August 2010 to complete the trade that brought Dan Haren to Los Angeles.
Skaggs made his big league debut in 2012, when he had six starts, but spent much of this year in the minors. He was 2-3 with a 5.12 ERA in seven starts this year for Arizona, leaving him with a 3-6 career mark.
Trumbo is eligible for salary arbitration for the first time this winter. Santiago is on track to be eligible after next season, Eaton following 2015 season and Skaggs after the 2016 season.
For Towers, the deal meant mission accomplished.
"We've got a guy that we can control now for three years. Two of the probably better right-handed power bats in the National League," he said, "Excited for spring training."